If the time period is doubled, then the angular momentum of the body will (provided the moment of inertia of the body is constant)

Options

A. remain constant
B. quadruple
C. become half
D. double

Explanation

To solve the problem of how the angular momentum of a body changes when the time period is doubled, we can follow these steps:

### Step 1: Understand the relationship between angular momentum, moment of inertia, and angular velocity.
The angular momentum \( L \) of a body is given by the formula:
\[ L = I \omega \]
where:
- \( L \) is the angular momentum,
- \( I \) is the moment of inertia,
- \( \omega \) is the angular velocity.

### Step 2: Relate angular velocity to the time period.
The angular velocity \( \omega \) is related to the time period \( T \) by the formula:
\[ \omega = \frac{2\pi}{T} \]
This means that if we know the time period, we can find the angular velocity.

### Step 3: Substitute the expression for angular velocity into the angular momentum formula.
Substituting \( \omega \) into the angular momentum formula gives:
\[ L = I \left( \frac{2\pi}{T} \right) \]
Thus, we can express angular momentum as:
\[ L = \frac{2\pi I}{T} \]

### Step 4: Analyze the effect of doubling the time period.
If the time period \( T \) is doubled, we have:
\[ T' = 2T \]
Now, substituting \( T' \) into the angular momentum formula:
\[ L' = \frac{2\pi I}{T'} = \frac{2\pi I}{2T} = \frac{2\pi I}{2} \cdot \frac{1}{T} = \frac{1}{2} \cdot \frac{2\pi I}{T} = \frac{1}{2} L \]

### Step 5: Conclusion
Thus, when the time period is doubled, the angular momentum \( L' \) becomes:
\[ L' = \frac{L}{2} \]
This means that the angular momentum of the body will be halved.

### Final Answer
The angular momentum of the body will be half of its original value when the time period is doubled.

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